Fascism has different faces in different countries, although they have some common features.
You guessed it right that modern Fascism has come out of a capitalist parliamentary system. It is a result of failure of the bourgeois government preceding the Fascist government to address some genuine problems of the masses. Fascists give lip service and address the mass that as soon as they come in power, they will work for solving those problems. Religious symbols, racial hatred are some crucial tools used by them to gain popularity of the majority. [Here's a detailed review on how Fascism arose in Germany. It's an article by Leon Trotsky.] [ Another article by Robin Blick on the development of German Fascism]